Discrete mixtures of normals pseudo maximum likelihood estimators of structural vector autoregressions

Likelihood inference in structural vector autoregressions with independent non-Gaussian shocks leads to parametric identification and efficient estimation at the risk of inconsistencies under distributional misspecification. We prove that autoregressive coefficients and (scaled) impact multipliers remain consistent, but the drifts and shocks' standard deviations are generally inconsistent. Nevertheless, we show consistency when the nonGaussian log-likelihood uses a discrete scale mixture of normals in the symmetric case, or an unrestricted finite mixture more generally, and compare the efficiency of these estimators to other consistent two-step proposals, including our own. Finally, our empirical application looks at dynamic linkages between three popular volatility indices.& COPY; 2022 Elsevier B.V. All rights reserved.

Automated summary

This paper examines likelihood inference in structural vector autoregressions with independent non-Gaussian shocks, finding that there may be inconsistencies in parameter estimation under distributional misspecification. We demonstrate that autoregressive coefficients and (scaled) impact multipliers remain consistent, but the drifts and shocks' standard deviations are generally inconsistent. However, we establish consistency when using a discrete scale mixture of normals or an unrestricted finite mixture in the non-Gaussian log-likelihood, and compare the efficiency of these estimators with other consistent two-step proposals, including our own. Finally, our empirical application investigates dynamic linkages between three popular volatility indices.